Single image crowd counting remains challenging primarily due to various issues, such as large scale variations, perspective and non-uniform crowd distribution. In this paper, we propose a novel architecture referred to Second-Order Convolutional Network (SOCN) to deal with this task from the perspective of improving the feature transformation capability of the network. The proposed SOCN applies a convolutional neural network as the backbone. We introduce three cascaded second-order blocks located behind the backbone to augment the family of transformation operations and increase the nonlinearity of the network, which can extract multi-scale and discriminative features. Furthermore, we design a context attention module (CAM) including dilated convolutions to assign weights to the score map of each second-order block for the purpose that the features which contribute to counting can be highlighted. We conduct various experiments on ShanghaiTeach1 and UCF_CC_502 datasets, and the results demonstrate the effectiveness of our method.